The accretion rates and mechanisms of Herbig Ae/Be stars · 2020. 1. 29. · ability properties...

The accretion rates and mechanisms of Herbig Ae/Be stars 1

The accretion rates and mechanisms of Herbig Ae/Be stars

C. Wichittanakom,1,2? R. D. Oudmaijer,2 J. R. Fairlamb,3 I. Mendigutıa,4

M. Vioque,2 and K. M. Ababakr51Department of Physics, Faculty of Science and Technology, Thammasat University, Rangsit Campus, Pathum Thani 12120, Thailand2School of Physics and Astronomy, EC Stoner Building, University of Leeds, Leeds LS2 9JT, UK3Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI, 96822, USA4Centro de Astrobiologıa (CSIC-INTA), Departamento de Astrofısica, ESA-ESAC Campus, PO Box 78,

28691 Villanueva de la Canada, Madrid, Spain5Erbil Polytechnic University, Kirkuk Road, Erbil, Iraq

Accepted 2020 January 07. Received 2020 January 01; in original form 2019 October 09

ABSTRACTThis work presents a spectroscopic study of 163 Herbig Ae/Be stars. Amongst these, we presentnew data for 30 objects. Stellar parameters such as temperature, reddening, mass, luminosity andage are homogeneously determined. Mass accretion rates are determined from Hα emission linemeasurements. Our data is complemented with the X-Shooter sample from previous studies andwe update results using Gaia DR2 parallaxes giving a total of 78 objects with homogeneouslydetermined stellar parameters and mass accretion rates. In addition, mass accretion rates of anadditional 85 HAeBes are determined. We confirm previous findings that the mass accretion rateincreases as a function of stellar mass, and the existence of a different slope for lower and highermass stars respectively. The mass where the slope changes is determined to be 3.98+1.37

−0.94 M�. Wediscuss this break in the context of different modes of disk accretion for low- and high mass stars.Because of their similarities with T Tauri stars, we identify the accretion mechanism for the late-type Herbig stars with the Magnetospheric Accretion. The possibilities for the earlier-type stars arestill open, we suggest the Boundary Layer accretion model may be a viable alternative. Finally,we investigated the mass accretion - age relationship. Even using the superior Gaia based data, itproved hard to select a large enough sub-sample to remove the mass dependency in this relationship.Yet, it would appear that the mass accretion does decline with age as expected from basic theoreticalconsiderations.

Key words: accretion, accretion discs – stars: formation – stars: fundamental param-eters – stars: pre-main-sequence – stars: variables: T Tauri, Herbig Ae/Be – techniques:spectroscopic

1 INTRODUCTION

Herbig Ae/Be stars (HAeBes) are optically visible interme-diate pre-main sequence (PMS) stars whose masses rangefrom about 2 to 10 M�. These PMS stars were first identi-fied by Herbig (1960), using three criteria: “Stars with spec-tral type A and B with emission lines; lie in an obscuredregion; and illuminate fairly bright nebulosity in its imme-diate vicinit”. HAeBes play an important role in understand-ing massive star formation, because they bridge the gap be-tween low-mass stars whose formation is relatively well un-derstood, and high-mass stars whose formation is still un-clear. The study of their formation is not well understood asmassive stars are very rare and as a consequence on averagefar away, and often optically invisible (Lumsden et al. 2013).

? E-mail: [email protected] (CW)

A long standing problem has also been that their brightnessis very high, such that radiation pressure can in principlestop accretion onto the stellar surface (Kahn 1974). More-over, they form very quickly and reach the main sequencebefore their surrounding cloud disperses (Palla & Stahler1993). This suggests that their evolutionary processes arevery different from T Tauri stars.

The accretion onto classical T Tauri low-mass stars ismagnetically controlled. The magnetic field from the startruncates material in the disc and from this point, materialfalls onto the star along the field line. After matter hits thephotosphere, it produces X-ray radiation that is absorbed bysurrounding particles. Then, these particles heat up and re-radiate at ultraviolet wavelengths, producing an UV-excessthat can be observed and from which the accretion luminos-ity can be calculated (Bouvier et al. 2007; Hartmann et al.2016). It was found later, that a correlation between theline luminosity and the accretion luminosity exists, allowing

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2 C. Wichittanakom et al.

accretion rates of classical T Tauri stars to be determinedfrom the UV-excess and absorption line veiling (Calvet et al.2004; Ingleby et al. 2013).

HAeBes have similar properties as classical TTauri stars, for instance having emission lines, UV-excess, a lower surface gravity than main-sequence stars(Hamann & Persson 1992; Vink et al. 2005) and they areusually identified by an infrared (IR) excess from circumstel-lar discs (Van den Ancker et al. 2000; Meeus et al. 2001).Because their envelopes are radiative, no magnetic fieldis expected to be generated in HAeBe stars as this usu-ally happens in stars by convection. Indeed, magnetic fieldshave rarely been detected towards them (Catala et al. 2007;Alecian et al. 2013). As a result magnetically controlled ac-cretion is not necessarily expected to apply in the case ofthe most massive objects, requiring another accretion mech-anism. However, how the material arrives at the stellar sur-face in the absence of magnetic fields is still unclear.

Several lines of evidence have indicated a difference be-tween the lower mass Herbig Ae and higher mass HerbigBe stars. Spectropolarimetric studies suggest that HerbigAe stars and T Tauri stars may form in the same process(Vink et al. 2005; Ababakr et al. 2017). Accretion rates ofHAeBes are determined from the measurement of UV-excess(Mendigutıa et al. 2011b) who have found that the relation-ship between the line luminosity and the accretion luminos-ity is similar to the classical T Tauri stars. A spectroscopicvariability study suggests that a Herbig Ae star is undergo-ing magnetospheric accretion in the same manner as classicalT Tauri stars (Scholler et al. 2016) while Mendigutıa et al.(2011a) find the Herbig Be stars to have different Hα vari-ability properties than the Herbig Ae stars. Therefore, mag-netically influenced accretion in HAeBes would still be pos-sible. A study employing X-shooter spectra for 91 HAeBeswas carried out by Fairlamb et al. (2015, 2017, hereafter F15and F17 respectively). They determined the stellar param-eters in a homogenous fashion, derived mass accretion ratesfrom the UV-excess and found the relationship between ac-cretion luminosity and line luminosity for 32 emission linesin the range 0.4–2.4 µm. 47 objects in their sample weretaken from The et al. (1994, table 1), which to this datecontains the strongest (candidate) members of the group.The Fairlamb papers were published before the Gaia par-allaxes became available, and the distances used may needrevision as these can affect parameters such as the radius,luminosity, stellar mass and mass accretion rate.

A Gaia astrometric study of 252 HAeBes was carriedout by Vioque et al. (2018) hereafter V18. They presentedparallaxes for all known HAeBes from the Gaia Data Release2 (Gaia DR2) Catalogue (Gaia Collaboration et al. 2016,2018). Also, they collected effective temperatures, opticaland infrared photometry, visual extinctions, Hα equivalentwidths, emission line profiles and binarities from the liter-ature. They derived distances, luminosities, masses, ages,infrared excesses, photometric variabilities for most of theirsample. This is the largest astrometric study of HAeBes todate. These Gaia DR2 parallaxes are useful for improvingthe stellar parameters of the previous studies.

The main aim of this paper is to determine stellar pa-rameters and accretion rates of 30 Northern HAeBes using ahomogeneous approach, extending the mostly Southern F15sample. In parallel, the results of F15 will be updated us-

ing the distances determined from the Gaia DR2 parallaxesand a redetermined extinction towards the objects. As such,this becomes the largest homogeneous spectroscopic anal-ysis of HAeBes to date. In addition, the accretion rates ofHAeBes in the V18 study are determined for the 104 objectsfor which Hα emission line equivalent widths are collectedfrom the literature or determined from archival spectra.

The structure of this paper is as follows. Section 2presents the spectroscopic data observation of all targets.Details of observations, instrumental setups and reductionprocedures are given in this section. Section 3 and 4 detailthe determination of stellar parameters and mass accretionrates. Sections 5 and 6 focus on the analysis and a discus-sion respectively. Section 7 provides a summary of the mainconclusions of this paper.

2 OBSERVATIONS AND DATA REDUCTION

2.1 IDS and sample selection

The data were collected in June 2013 using the IntermediateDispersion Spectrograph (IDS) instrument and the RED+2CCD detector with 2048 × 4096 pixels (pixel size 24 µm),which is attached to the Cassegrain focus of the 2.54-m IsaacNewton Telescope (INT) at the Observatorio del Roque delos Muchachos, La Palma, Spain. The observations spannedsix nights between the 20th and the 25th June 2013. Biasframes, flat field frames, object frames and arc frames ofCu-Ar and Cu-Ne comparison lamp were taken each nightto prepare for the data reduction.

In the first two nights the spectrograph was set up witha 1200 lines mm−1 R1200B diffraction grating and a 0.9 or1.0 arcsecond wide slit in order to obtain spectra across theBalmer discontinuity. The wavelength coverage was 3600–4600 A, centred at 4000.5 A. In this range the hydrogen linesof Hγ,Hδ, H(7-2), H(8-2), H(9-2) and H(10-2) can be anal-ysed. This combination provides a reciprocal dispersion of0.53 A pixel−1 with a spectral resolution of ∼ 1 A and a re-solving power of R ∼ 4000.

For the next two nights the R1200Y grating was used toobserve spectra in the visible. Its spectral range covers 5700to 6700 A, centred at 6050.4 A. This range includes the He iline at 5876 A, the [O iλ6300] line and the Hα line at 6562 A.This setup results in a reciprocal dispersion of 0.52 A pixel−1

and a resolving power of R ∼ 6500. The final 2 nights usedthe R1200R grating to observe the spectral range of 8200–9200 A, centred at 8597.2 and 8594.4 A. This range coversthe O i line at 8446 A, all lines of the Ca ii triplet and manylines of the Paschen series. With this setup the reciprocaldispersion becomes 0.51 A pixel−1, giving a resolving powerof R ∼ 9000.

The sample consists of 45 targets, with 30 HAeBes, and15 standard stars. 26 Herbig stars were chosen from the cat-alogue of The et al. (1994, table 1) and 4 from Vieira et al.(2003). About 67 per cent of HAeBes in the final sample arein the northern hemisphere. There are 7 HAeBes which arealso in the sample of F15. Spectra of standard stars wereobserved each night for spectral comparisons. A log of theobservations of the 30 HAeBes is shown in Table 1 whilea log of the observations of the standard stars is presentedin Table A1 (See Appendix A in the online version of thispaper).

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Table 1. Log of observations of 30 HAeBes. Column 1 gives the object name. Columns 2 and 3 are right ascension (RA) in the units of time (.h .m .s) and declination (DEC) in the units

of angle (.◦ .′ .′′) respectively. Column 4 lists the observation dates. Columns 5–7 present the exposure times for each grating. The signal-to-noise ratios for each grating are given incolumns 8–10. These were determined using a 20 A wide line free spectral regions centred at the wavelength 4200, 6050 and 8800 A for R1200B, R1200Y and R1200R grating respectively.

Spectral types and photometry are listed along with references in columns 11–16.

Name RA DEC Obs Date Exposure Time (s) SNR Spectral Type Photometry (mag)

(J2000) (J2000) (June 2013) R1200B R1200Y R1200R B Y R B V Rc R Ic

V594 Cas 00:43:18.3 +61:54:40.1 21; 23; 24 600 600 600 152 160 50 B81 11.08 10.51 10.08 - 9.5513

PDS 144 15:49:15.3 -26:00:54.8 22; 24 - 900 900 - 97 83 A5 V2 13.28 12.79 12.49 - 12.162

HD 141569 15:49:57.8 -03:55:16.3 20; 22; 24 60 60 60 302 385 194 A0 Ve3 7.23 7.13 7.08 - 7.022

HD 142666 15:56:40.0 -22:01:40.0 20; 22; 24 90; 180 90; 150 150 19 147 47 A8 Ve3 9.17 8.67 8.35 - 8.012

HD 145718 16:13:11.6 -22:29:06.7 21; 23; 25 90 180 180 30 160 74 A8 IV2 9.62 9.10 8.79 - 8.452

HD 150193 16:40:17.9 -23:53:45.2 21; 23; 24; 25 90 300 120; 300 54 258 96 A2 IVe3 9.33 8.80 8.41 - 7.9314

PDS 469 17:50:58.1 -14:16:11.8 23; 25 - 1200 1200 - 127 62 A02 13.33 12.77 12.39 - 11.952

HD 163296 17:56:21.3 -21:57:21.9 20; 23; 24; 25 60 60 60 60 270 125 A1 Vep3 6.94 6.83 6.77 - 6.7314

MWC 297 18:27:39.5 -03:49:52.1 21; 22; 24; 25 900 10; 60 1200; 600 22 16 102 B02 14.28 12.03 10.19 - 8.8014

VV Ser 18:28:47.9 +00:08:39.8 21; 23; 25 900 600 600 91 180 113 B64 12.82 11.81 11.10 - 10.3113

MWC 300 18:29:25.7 -06:04:37.3 21; 23; 25 900 600; 60 600 48 29 19 B1 Ia+[e]5 12.81 11.78 11.09 - 10.5814

AS 310 18:33:21.3 -04:58:04.8 20; 22; 24 40; 900 1200 1200 35 144 128 B1e4 13.56 12.59 11.93 - 11.2014

PDS 543 18:48:00.7 +02:54:17.1 21; 22; 24 900 1200 1200 39 153 149 B12 14.56 12.52 11.25 - 9.962

HD 179218 19:11:11.3 +15:47:15.6 21; 23; 25 60 120 120 140 311 166 A0 IVe3 7.47 7.39 7.34 - 7.292

HD 190073 20:03:02.5 +05:44:16.7 21; 23; 25 60 120 120; 300 65 205 90 A0 IVp+sh2 7.86 7.73 - 7.6615 -

V1685 Cyg 20:20:28.2 +41:21:51.6 20; 22; 24; 25 600 600; 60 600; 60 120 114 82 B2 Ve3 11.48 10.69 - 9.6316 -

LkHA 134 20:48:04.8 +43:47:25.8 20; 22; 24 600 600 600 79 192 95 B86 12.02 11.35 - 10.5616 -

HD 200775 21:01:36.9 +68:09:47.8 20; 22; 24; 25 60 60; 30 30; 60 161 192 50 B34 7.77 7.37 - 6.8416 -

LkHA 324 21:03:54.2 +50:15:10.0 21; 23; 25 900 1200 1200 52 166 123 B84 13.71 12.56 11.85 - 11.0913

HD 203024 21:16:03.0 +68:54:52.1 21; 23; 24; 25 120 180 180 56 187 65 A5 V3 9.24 9.01 9.02 - 8.6217

V645 Cyg 21:39:58.3 +50:14:20.9 21; 23; 25 900 1200 1200 20 86 152 O8.57 14.55 13.47 - 12.2816 -

V361 Cep 21:42:50.2 +66:06:35.1 20; 22; 24; 25 300 300 300 146 219 84 B44 10.65 10.21 9.89 - 9.5013

V373 Cep 21:43:06.8 +66:06:54.2 20; 22; 24 900 1200 1200 96 143 103 B88 13.22 12.33 11.7 - 11.0113

V1578 Cyg 21:52:34.1 +47:13:43.6 21; 23; 24; 25 300 300; 600 300 86 225 191 A04 10.53 10.13 - 9.6716 -

LkHA 257 21:54:18.8 +47:12:09.7 20; 22; 23; 24 900 1200 1200 54 179 129 A2e9 14.00 13.29 12.86 - 12.3917

SV Cep 22:21:33.2 +73:40:27.1 20; 22; 24 240 300 300 87 188 112 A2 IVe3 11.37 10.98 - 10.5816 -

V375 Lac 22:34:41.0 +40:40:04.5 23; 25 - 1200 1200 - 109 71 A7 Ve10 14.22 13.38 12.84 - 12.2513

HD 216629 22:53:15.6 +62:08:45.0 20; 22; 24 90 180 180 91 251 110 B3 IVe+A311 10.01 9.28 - 8.5316 -

V374 Cep 23:05:07.5 +62:15:36.5 20; 22; 24 600 450 450 121 173 138 B5 Vep12 11.14 10.28 9.71 - 9.1217

V628 Cas 23:17:25.6 +60:50:43.4 21; 23; 24; 25 900 600; 60 600 26 130 149 B0eq1 12.63 11.37 10.38 - 9.3713

References. (1) Hillenbrand et al. (1992); (2) Vieira et al. (2003); (3) Mora et al. (2001); (4) Hernandez et al. (2004); (5) Wolf & Stahl (1985); (6) Herbig (1958); (7) Clarke et al. (2006); (8)

Dahm & Hillenbrand (2015); (9) Walker (1959); (10) Calvet & Cohen (1978); (11) Skiff (2014); (12) Garrison (1970); (13) Fernandez (1995); (14) De Winter et al. (2001); (15) Oudmaijer et al.

(2001); (16) Herbst & Shevchenko (1999); (17) Zacharias et al. (2012).

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The data reduction was performed using the Image Re-duction and Analysis Facility (IRAF1). Standard procedureswere used in order to process all frames. Generally, thereare three steps of data reduction; bias subtraction, flat fielddivision and wavelength calibration. First, many bias frameswere taken and averaged to reduce some noise and the biaslevel was removed from the CCD data. Next, flat field divi-sion was used to remove the variations of CCD signal in eachpixel. All flat frames were averaged before subtracting thebias. Then, all of the object frames were divided by the nor-malised flat-field frame in order to correct the pixel-to-pixelvariation of the detector sensitivity. The object frame wasextracted to a one-dimensional spectrum by defining the ex-traction aperture on the centre of the profile and subtractingthe sky background. Finally, the data were wavelength cali-brated. The accuracy of the wavelength calibration is mea-sured from an RMS of the fit and is less than 10 per cent ofthe reciprocal dispersion (< 0.05 A pixel−1). For illustration,the Hα profiles of all 30 objects are displayed in Figure B1(See Appendix B in the online version of this paper).

3 STELLAR PARAMETERS AND MASSACCRETION RATE DETERMINATIONS

Measurement of accretion rates requires accurate stellar pa-rameters of the star in question. Therefore, this section aimsto determine accretion rates by first determining the stellarparameters, such as the effective temperature, surface grav-ity, distance, radius, reddening, luminosity, mass and age.These will be determined by combining the IDS spectra,stellar model atmosphere grids, photometry from the litera-ture, the Gaia DR2 parallaxes and stellar isochrones.

3.1 Effective temperature and surface gravity

To estimate the effective temperature of the target, a com-parison of the known standard star spectra with the un-known target spectrum is performed. The list of standardstars including spectral types is shown in Table A1 (See Ap-pendix A in the online version of this paper). The conversionfrom the spectral type to effective temperature can be foundfrom Straizys & Kuriliene (1981). Then, the range of effec-tive temperatures was explored in more detail with spectracomputed from model atmospheres.

The model atmospheres used in this work aregrids of BOSZ-Kurucz model atmospheres computed byBohlin et al. (2017). The BOSZ models are calculated fromATLAS-APOGEE ATLAS9 (Meszaros et al. 2012) whichcame from the original ATLAS code version 9 (Kurucz1993). The metallicity [M/H] = 0, carbon abundance [C/H] =

0, alpha-element abundance [α/H] = 0, microturbulent ve-locity ξ = 2.0 km s−1, rotational broadening velocity v sin i =

0.0 km s−1, and instrumental broadening R = 5000 areadopted. This instrumental broadening is chosen for match-ing the resolution of the blue spectra. The range of effec-tive temperature Teff is from 3500 K to 30000 K with steps

1 IRAF is distributed by the National Optical Astronomy Obser-

vatory, which is operated by the Association of Universities forResearch in Astronomy (AURA) under a cooperative agreement

with the National Science Foundation.

of 250 K (from 3500 K to 12000 K), 500 K (from 12000 K to20000 K) and 1000 K (from 20000 K to 30000 K). The rangeof surface gravity log(g) is from 0.0 dex to 5.0 dex with stepsof 0.5 dex. By using linear interpolation, log(g) with steps of0.1 dex were calculated.

The procedure to obtain the effective temperature andsurface gravity in this work follows the same method by F15.The effective temperature and surface gravity determinationis carried out by primarily comparing the wings of the ob-served hydrogen Balmer lines Hγ, Hδ and Hε with syntheticprofiles produced with solar metallicity from BOSZ models.The shapes of the hydrogen profiles are not very sensitive tometallicity (Bohlin et al. 2017) while their widths are dom-inated by pressure broadening, while rotation hardly affectsthe shapes. Hα is not used for spectral typing because itis frequently strongly in emission for HAeBes. This phe-nomenon can affect the shape of the wings and cause dif-ficulty of fitting the BOSZ models to target spectra. Hβ isalso not used for spectral typing because it appears aroundthe edge of the blue spectrum which makes a proper char-acterization of Hβ’s line profile troublesome.

In order to carry out the fitting, both the observed pro-files and the synthetic profiles are normalised based on thecontinuum on both the blue and red side of the profile. Next,the observed wavelengths of the target profiles were cor-rected to the vacuum wavelength of the synthetic profileusing the IRAF DOPCOR task. The effective temperatureand surface gravity are obtained from the fit of the nor-malised synthetic spectra to the normalised observed spec-tra by considering continuum features and the wings of theprofile above the normalised intensity of 0.8. This intensitywas chosen because this part of the wings is sensitive to vari-ation of the log(g) while the central part of the profile of aHerbig Ae/Be star can be contaminated by emission.

The width of the Balmer lines depends upon both effec-tive temperature and surface gravity. Different combinationsof Teff and log(g), can create the same width. This degener-acy can be solved by visual inspection of absorption featuresin the wings and continuum either side of the lines. The finalvalue for the effective temperature and surface gravity arethe average value of the best fit for each profile (Hγ, Hδ andHε). The uncertainties of Teff and log(g) were chosen to bethe typical difference in the values determined for the threelines respectively. If the standard error becomes zero or lessthan that, the step size will be adopted. An example of spec-tral typing by fitting the Balmer line profile of HD 141569(black) and the BOSZ model (blue) is demonstrated in Fig-ure 1.

For a given Teff , normally, the higher the log(g), thebroader the Balmer profile. Therefore, the region of thewings of the hydrogen profile near the continuum level can beused to obtain both effective temperature and surface grav-ity as was mentioned earlier. Unfortunately, there is a non-linear relationship between the surface gravity and width ofthe Balmer profile for objects that have Teff < 8000 K. Forthis reason, a spectroscopic log(g) can not be determinedand the surface gravity is calculated instead using the stel-lar mass and radius (see later). For 3 objects (PDS 144S,PDS 469 and V375 Lac) no near UV blue spectra were takenduring the observations. Fortunately, a FEROS spectrum of

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Figure 1. The normalised spectrum of HD 141569 fits with BOSZmodel of Teff = 9500 K and log(g) = 4.2.

PDS 4692 was found in the ESO Science Archive Facility andwas used to determine temperature and surface gravity. Inthe case of PDS 144S and V375 Lac, visible spectra includ-ing Hα profiles in combination with spectral types from theliterature were investigated in order to adopt their effectivetemperatures.

7 objects show extremely strong emission lines. Thesestrong emissions have an influence on the wings on even thewhole Balmer profiles. Both Teff and log(g) could thereforenot be determined by this method. Instead, for these objects,estimated temperatures from the literature are adopted. Thestars for which this process is performed on are noted in thelast column of Table 2.

There are 7 objects in this work that overlap with F15.The difference in temperatures of these objects is on aver-age 180 K, which is smaller than the step-size used by bothstudies. Figure 2 compares the effective temperature derivedin this work (Table 2) with estimated values from the liter-ature. The good correlation would suggest that our methodis reliable, the fact that it is applied to the entire sampleensures a homogeneous study.

3.2 Visual extinction, distance and radius

The second step is to use the synthetic BOSZ spectral energydistribution and previous photometry results to determinethe visual extinction or reddening (AV ) by fitting the syn-thetic surface flux density to observed photometry. In thecase of zero extinction or for extinction corrected photome-try, the flux density f of the BOSZ model and the observedfluxes differ by the ratio of distance to the star and its ra-dius (D/R∗). The spectral energy distribution grid of the

2 Based on observations collected at the European Southern Ob-

servatory under ESO programmes 084.A-9016(A).

Figure 2. The effective temperature derived in this work com-pared to temperatures derived from spectral types in the lit-

erature listed in Table 1 and Table A1. The spectral type

was converted to temperature using the values provided inStraizys & Kuriliene (1981), and an uncertainty of a subclass of

spectral type was assigned for the temperature. HAeBes and stan-

dard stars are denoted in circle and square respectively. Circleswith larger circle around them indicate the objects that tempera-

ture from Fairlamb et al. (2015) is used. The standard deviation(σ) between both log(Teff ) is only 0.02. The solid line is the ex-

pected line of correlation and the dashed lines are 3σ deviation

from the solid line.

BOSZ models are set up for the effective temperatures fromthe previous step with a range of scaling factors D/R∗. Thevalue of log(g) does not have a significant effect on the spec-tral energy distribution shape. Therefore, log(g) = 4.0 wasadopted at this stage.

The observed photometry is dereddened using the ex-tinction values Aλ/AV from Cardelli et al. (1989) with thestandard ratio of total to selective extinction parameterRV = 3.1 and zero-magnitude fluxes from Bessell (1979).By varying AV in steps of 0.01 magnitude, the best fit of thephotometry and BOSZ models will then yield the best fit-ting reddening values. Only the BVRI magnitudes are used,as the U-band and JHKLM photometry are often affected bythe Balmer continuum excess and IR-excess emission respec-tively, i.e. they can not automatically be used in the fitting.All of the observed BVRcIc or BVR photometry from theliterature are shown in Table 1. For 3 objects (HD 203024,LkHA 257 and V374 Cep) their Sloan photometry needed tobe converted to Johnson-Cousins photometry. This was doneusing the transformation equations provided by Smith et al.(2002). The uncertainties in the resulting AV and D/R∗ areassigned to be at values that resulted twice of the minimumchi-squared value. Figure 3 demonstrates an example of pho-tometry fitting.

The scaling factor D/R∗ allows us to calculate stellarradius R∗, provided the stellar distance D is known. TheGaia DR2 catalogue provides astrometric parameters, such

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Figure 3. The synthetic spectral energy distribution BOSZ

model (black line) is fitted to the dereddened photometry (red

point) of HD 141569. The observed BVRc Ic photometry ofHD 141569 were taken from Vieira et al. (2003). A synthetic

spectral energy distribution BOSZ model with Teff = 9500 K and

log(g) = 4.0 is fitted to the dereddened photometry. This pro-vides the reddening AV = 0.38+0.02

−0.03 mag and the scaling factor

D/R∗ = 63.7+1.1−0.7 pc/R� .

as positions, proper motions and parallaxes for more than1.3 billion targets including most of the known HAeBes. Thedistances to most of our targets were determined by V18using Gaia DR2 parallaxes. Re-normalised unit weight error(RUWE) is used to select sources with good astrometry. Weadopted RUWE < 1.4 as a criterion for good parallaxes (seeGaia Data Release 2 document). 7 stars have low qualityparallaxes, and for 2 stars no parallaxes are presented in theGaia archive. These are noted in the final column of Table 2.In total, stellar radii could be determined for 26 out of the30 targets.

3.3 Stellar luminosity, mass and age

Using the stellar radius R∗ and the effective temperatureTeff , the luminosity L∗ can be determined from the Stefan-Boltzmann law. The next step is to estimate the massand age of the HAeBes using isochrones. Stellar isochronesof Marigo et al. (2017) from 0.01 to 100 Myr are used inorder to extract a mass and an age of the target fromthe luminosity-temperature Hertzsprung-Russell diagram. Ametallicity Z = 0.01 and helium mass fraction Y = 0.267 arechosen, because these values are close to solar values.

After each star is placed on the HR diagram, the twoclosest points on an isochrone are used to obtain the mass ofthe star by interpolating between those points. Uncertain-ties of mass and age are derived from the error bars of theeffective temperature Teff and the luminosity L∗ on the HRdiagram. All determined parameters of all targets are pre-sented in Table 2. The positions of the 21 HAeBes on theHR diagram are represented with red symbols in Figure 4 As

mentioned above, the 9 targets that are not included in theplot have low quality parallaxes or do not have parallaxes atall. Since the 3 objects (HD 142666, HD 145718 and SV Cep)have had Teff < 8000 K, their surface gravity cannot be de-termined from fitting the spectra with stellar atmosphericmodels. Instead, their surface gravities were calculated fromthe stellar mass and radius derived from the parallexes in-stead. These are also noted in the log(g) column of Table 2.

3.4 Extending the sample with HAeBes in thesouthern hemisphere

The original driver for the INT observations presented herewas to extend the spectroscopic analysis of the, mostlysouthern, sample of F15 to the northern hemisphere. How-ever, F15 determined spectroscopic distances using theirspectral derived values of the surface gravity or literaturevalues for the distances to their 91 HAeBes. The availabilityof Gaia-derived distances warrants a re-determination of thestellar parameters. To this end we use the distances from theGaia DR2 parallax (V18). In parallel, we re-assessed the ex-tinction values using the same photometric bands BVRcIcas above to ensure consistency in the determination of theextinction. Most of the photometry used for the photometryfitting can be found in Fairlamb et al. (2015, table A1). Wecollated Sloan photometry from Zacharias et al. (2012) for3 objects (HD 290500, HT CMa and HD 142527) and oneobject, HD 95881, from APASS3 DR10 and converted theseto the Johnson-Cousins system. Moreover, we also used thebrightest V-band magnitude of Johnson BVR photometryfor 2 objects, HD 250550 and KK Oph, and Johnson BVRIphotometry for Z CMa from Herbst & Shevchenko (1999).The redetermined stellar parameters for the 91 HAeBes fromF15 are listed in Table C1 (See Appendix C in the onlineversion of this paper). For the sample as a whole, the lumi-nosities resulting from the revised distances and extinctionsare on average similar to the original F15 values, howeverthe contribution to the scatter around the mean differencesis dominated by the new distances. We thus conclude thatthe improvement in distance values dominates that of theextinction when arriving at the final luminosities.

We now have the largest spectroscopic sample ofHAeBes and the homogeneously determined stellar parame-ters including mass accretion rates, which will be determinedin the next section. 7 targets in F15’s sample which are alsoin this work’s sample were left out, leaving 84 HAeBes intheir sample. Unfortunately, 22 out of the 84 objects (notincluding PDS 144S) have low quality or do not have a GaiaDR2 parallax. These objects cannot be placed on the HRdiagram at this stage. The final sample contains 83 Her-big Ae/Be objects. Figure 4 demonstrates all these HAeBes(21 + 62) placed in the HR diagram. Many targets are gath-ered around 2 M� and few targets are located at high-masstracks. This can be understood by the initial mass func-tion IMF (Salpeter 1955). Low-mass stars are more com-mon than high-mass stars. Moreover, low-mass stars evolveslower across the HR diagram.

3 https://www.aavso.org/apass-dr10-download

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Table 2. Determined stellar parameters. Columns 2–9 are effective temperature, surface gravity, visual extinction, distance, radius,luminosity, mass and age respectively. Distance D in column 5 is obtained from Vioque et al. (2018).

Name Teff log(g) AV D R∗ log(L∗ ) M∗ Age

(K) [cm s−2] (mag) (pc) (R�) [L� ] (M�) (Myr)

V594 Cas 11500+250−250 3.70+0.10

−0.10 2.27+0.18−0.23 569+16

−14 3.86+0.52−0.53 2.37+0.15

−0.17 3.51+0.45−0.42 1.29+0.53

−0.38

PDS 144S 7750+500−500

a 4.00+0.30−0.30 1.02+0.07

−0.07 -d - - - -

HD 141569 9500+250−250 4.20+0.10

−0.10 0.38+0.02−0.03 110.63+0.91

−0.88 1.74+0.03−0.04 1.34+0.06

−0.07 2.06+0.02−0.15 5.89+1.87

−0.64

HD 142666 7250+250−250 4.00+0.10

−0.10c 0.82+0.07

−0.08 148.3+2−1.9 2.21+0.11

−0.12 1.08+0.10−0.11 1.64+0.12

−0.11 7.76+1.79−1.30

HD 145718 7750+250−250 4.20+0.10

−0.10c 1.10+0.06

−0.06 152.5+3.2−3 1.85+0.10

−0.10 1.05+0.10−0.10 1.62+0.07

−0.03 8.71+0.84−1.12

HD 150193 9250+250−250 4.10+0.10

−0.10 1.88+0.16−0.20 150.8+2.7

−2.5 2.34+0.26−0.27 1.56+0.14

−0.15 2.12+0.21−0.12 4.57+0.93

−1.02

PDS 469 9500+750−750

a 3.80+0.30−0.30 1.94+0.12

−0.13 -d - - - -

HD 163296 9000+250−250 4.10+0.10

−0.10 0.29+0.01−0.02 101.5+2

−1.9 1.87+0.05−0.05 1.31+0.07

−0.07 1.95+0.07−0.07 6.03+0.28

−0.27

MWC 297 24000+2000−2000

b 4.00+0.10−0.10 7.87+0.41

−0.64 375+22−18 9.28+3.12

−3.04 4.41+0.39−0.50 14.53+6.11

−4.84 0.04+0.07−0.02

VV Ser 14000+1000−1000 4.30+0.30

−0.30 3.74+0.22−0.27 -d - - - -

MWC 300 23000+2000−2000

b 3.00+0.20−0.20 3.85+0.21

−0.28 1400+250−160 6.02+1.96

−1.44 3.96+0.39−0.39 10.09+3.76

−1.89 0.09+0.09−0.05

AS 310 26000+2000−2000 4.40+0.35

−0.35 3.86+0.20−0.24 2110+350

−240 5.70+1.71−1.27 4.13+0.36

−0.36 11.60+3.92−2.18 0.07+0.08

−0.04

PDS 543 28500+2500−2500

b 4.00+0.10−0.10 7.11+0.28

−0.40 1410+240−160 16.24+5.99

−4.57 5.19+0.42−0.45 30.02+18.28

−10.85 0.01+0.01−0.01

HD 179218 9500+250−250 3.95+0.10

−0.10 0.33+0.02−0.02 266+5.6

−5.2 3.62+0.12−0.11 1.98+0.07

−0.07 2.86+0.16−0.20 2.04+0.47

−0.26

HD 190073 9750+250−250 3.50+0.10

−0.10 0.20+0.04−0.04 870+100

−70 9.23+1.28−0.94 2.84+0.16

−0.14 5.62+0.78−0.65 0.28+0.14

−0.10

V1685 Cyg 23000+4000−4000

b 4.06+0.10−0.10 3.33+0.34

−0.51 910+46−39 5.48+1.51

−1.51 3.88+0.49−0.61 9.53+4.57

−2.55 0.11+0.27−0.07

LkHA 134 11000+250−250 4.00+0.10

−0.10 2.44+0.19−0.24 843+36

−31 4.53+0.71−0.70 2.43+0.17

−0.19 3.77+0.56−0.56 1.02+0.60

−0.34

HD 200775 19000+3000−3000 4.27+0.25

−0.25 1.85+0.15−0.17 -d - - - -

LkHA 324 12500+500−500 4.00+0.10

−0.10 3.94+0.14−0.16 605+16

−14 3.15+0.34−0.33 2.34+0.16

−0.17 3.36+0.41−0.30 1.51+0.49

−0.41

HD 203024 8500+500−500 3.83+0.29

−0.29 0.52+0.24−0.31 -e - - - -

V645 Cyg 30000+7000−7000

b 3.75+0.35−0.35 4.21+0.29

−0.40 -d - - - -

V361 Cep 16750+500−500 4.00+0.10

−0.10 1.97+0.14−0.15 893+35

−31 4.34+0.52−0.48 3.12+0.15

−0.15 5.56+0.65−0.57 0.40+0.16

−0.11

V373 Cep 11500+1250−1250

b 3.50+0.50−0.50 3.24+0.20

−0.23 -d - - - -

V1578 Cyg 10500+500−500 3.80+0.20

−0.20 1.46+0.08−0.08 773+30

−27 4.77+0.41−0.37 2.39+0.15

−0.15 3.74+0.45−0.41 1.02+0.39

−0.28

LkHA 257 9250+250−250 4.05+0.10

−0.10 2.28+0.07−0.08 794+18

−16 1.84+0.11−0.11 1.35+0.10

−0.10 1.98+0.06−0.04 5.76+1.32

−0.51

SV Cep 8000+500−500 4.37+0.11

−0.11c 0.78+0.04

−0.05 344.3+4−3.8 1.48+0.05

−0.06 0.91+0.14−0.15 1.63+0.04

−0.14 11.00+10.40−2.49

V375 Lac 8000+750−750

a 4.30+0.10−0.10 2.31+0.14

−0.16 -e - - - -

HD 216629 21500+1000−1000 4.00+0.10

−0.10 2.86+0.13−0.15 805+31

−27 7.59+0.94−0.83 4.04+0.18

−0.18 10.83+1.71−1.54 0.07+0.04

−0.02

V374 Cep 15500+1000−1000 3.50+0.10

−0.10 3.20+0.15−0.18 872+40

−35 7.72+1.05−0.98 3.49+0.22

−0.23 7.50+1.46−1.28 0.16+0.12

−0.06

V628 Cas 31000+5000−5000

b 4.00+0.10−0.10 5.05+0.36

−0.55 -d - - - -

Notes. (a) Stars for which NUV-B spectra were not obtained. (b) Stars which display extremely strong emission lines. (c) Stars for

which parallactic log(g) is used. (d) Stars which have low quality parallaxes in the Gaia DR2 Catalogue (see the text for discussion). (e)

Stars which do not have parallaxes in the Gaia DR2 Catalogue.

3.5 Combining with additional HAeBes with GaiaDR2 data from V18

In order to expand the sample further, the rest of 144/252objects in the sample of V18 were investigated. There are101 objects which satisfy the condition RUWE < 1.4. Theyare also included in Figure 4. Hα equivalent widths are pro-vided for most objects in Vioque et al. (2018, their table 1and table 2) with references. Spectra for 14 objects withoutHα data in the V18 sample were found in the ESO ScienceArchive Facility. These were downloaded and their Hα EWswere measured. The stellar radii and surface gravities werecalculated using the temperatures, luminosities and massesprovided in V18. The intrinsic equivalent widths were mea-

sured from BOSZ models for the temperature provided inVioque et al. (2018, table 1 and table 2) and the calculatedsurface gravity. This will enable us to compute mass accre-tion rates for a further 85 objects below. Table D1 presentsall of the emission lines measurements and determined accre-tion rates of the V18 sample (See Appendix D in the onlineversion of this paper).

4 ACCRETION RATE DETERMINATION

We now will determine the mass accretion rates of the com-bined sample of Herbig Ae/Be stars. The underlying as-

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Figure 4. The placement of all 184 HAeBes in the HR diagram. The red circles are this work sample of 21 HAeBes, whereas 62 HAeBes

in the sample of Fairlamb et al. (2015) are denoted as the blue circles and 101 HAeBes in Vioque et al. (2018) are shown as the greencircles. All of these objects satisfy the condition RUWE < 1.4. The PMS tracks with initial mass from 1 to 40 M� (Bressan et al. 2012;

Tang et al. 2014) are plotted as solid lines and isochrones of 0.01, 0.1, 1 and 10 Myr (Marigo et al. 2017) are plotted as dashed lines.

sumption of the methodology is that the stars accrete mate-rial according to the MA paradigm, which, as demonstratedby Muzerolle et al. (2004), can explain the observed excessfluxes in Herbig Ae/Be stars. The infalling material shock-ing the photosphere gives rise to UV-excess emission, whosemeasurement can be converted into an accretion luminosity.Knowledge of the stellar parameters can then return a valueof the mass accretion rate.

F15 derived the accretion rates for their sample fromthe UV excess following the methodology of Muzerolle et al.(2004) and extending the work of Mendigutıa et al. (2011b).Unfortunately, as mentioned before, our current observa-tional set-up did not allow for such accurate measurements.However, as for example pointed out by Mendigutıa et al.(2011b), the accretion luminosity correlates with the linestrengths of various types of emission lines. They will there-fore also correlate with the mass accretion rate (see alsoFairlamb et al. 2017). As such, the line strengths do providean observationally cheap manner to derive the accretion rateof an object without having to resort to the rather delicateand time-consuming process of measuring the UV excess.We should note that despite this, it is not clear whether theobserved correlation is intrinsically due to accretion or someother effect (Mendigutıa et al. 2015a).

We have chosen the Hα line for the accretion luminos-ity determination, as these lines are strongest lines presentin the spectra. To arrive at a measurement of the total line

emission, we need to take account of the fact that the un-derlying line absorption is filled in with emission. Therefore,the intrinsic absorption equivalent width EWint needs to besubtracted from the observed equivalent width EWobs. Theintrinsic EW is measured from the synthetic spectra corre-sponding to the effective temperature and surface gravitydetermined earlier.

The line luminosity Lline was calculated using the unred-dened stellar flux at the wavelength of Hα and distance tothe star. The relationship between accretion luminosity andline luminosity goes as (cf. e.g. Mendigutıa et al. 2011b).

log(

LaccL�

)= A + B × log

(LlineL�

), (1)

where A and B are constants corresponding to the inter-cept and the gradient of the relation between log(Lacc/L� )and log(Lline/L� ) respectively. This relationship has, mostrecently, been determined for 32 accretion diagnostic emis-sion lines by F17. For the case of Hα, the constants areA = 2.09 ± 0.06 and B = 1.00 ± 0.05. The mass accretion rateis then determined from the accretion luminosity, stellar ra-dius and stellar mass by Equation 2.

Macc =LaccR∗GM∗

(2)

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Table 3 summarises the EW measurements for the Hαline and mass accretion rates in all HAeBes.

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10C.Wichittan

akomet

al.

Table 3. The equivalent width measurements and accretion rates. Column 2 provides the Hα emission line profile classification scheme according to Reipurth et al. (1996): single-peaked

(I); double-peaked and the secondary peak rises above half strength of the primary peak (II); double-peaked and the secondary peak rises below half strength of the primary peak (III),

when the secondary peak is located blueward or redward of the primary peak, class II and III are label with B or R respectively; regular P-Cygni profile (IV B); and inverse P-Cygniprofile (IV R). The classifications are based on the emission lines in Figure B1 corrected for absorption. Columns 3–10 present observed equivalent width, intrinsic equivalent width,

corrected equivalent width, continuum flux density at central wavelength of the Hα profile, line flux, line luminosity, accretion luminosity and mass accretion rate respectively.

Name Hα EWobs EWint EWcor Fλ Fline log(Lline) log(Lacc) log(Macc)

profile (A) (A) (A) (W m−2 A−1) (W m−2) [L� ] [L� ] [M� yr−1]

V594 Cas IV B −81.79 ± 1.23 8.21 ± 0.19 −90.00 ± 1.24 1.11 × 10−15 (9.96 ± 0.14) × 10−14 0.00+0.03−0.03 2.09+0.09

−0.09 −5.36+0.09−0.10

PDS 144S I −14.55 ± 0.53 12.82 ± 0.14 −27.37 ± 0.55 4.70 × 10−17 (1.29 ± 0.03) × 10−15 - - -

HD 141569 II R 6.38 ± 0.01 14.80 ± 0.26 −8.42 ± 0.26 4.17 × 10−15 (3.51 ± 0.11) × 10−14 −1.87+0.02−0.02 0.22+0.17

−0.18 −7.35+0.18−0.15

HD 142666 IV R 2.46 ± 0.08 11.01 ± 0.17 −8.54 ± 0.19 1.84 × 10−15 (1.57 ± 0.04) × 10−14 −1.97+0.02−0.02 0.12+0.18

−0.18 −7.24+0.17−0.17

HD 145718 I 10.83 ± 0.42 14.18 ± 0.25 −3.35 ± 0.49 1.50 × 10−15 (5.03 ± 0.73) × 10−15 −2.44+0.08−0.09 −0.35+0.26

−0.27 −7.79+0.26−0.29

HD 150193 III B −0.29 ± 0.05 14.86 ± 0.18 −15.15 ± 0.19 3.85 × 10−15 (5.83 ± 0.07) × 10−14 −1.38+0.02−0.02 0.71+0.15

−0.15 −6.75+0.15−0.18

PDS 469 I 4.65 ± 0.17 13.50 ± 0.17 −8.85 ± 0.24 1.02 × 10−16 (9.04 ± 0.24) × 10−16 - - -

HD 163296 I −11.04 ± 0.87 15.48 ± 0.13 −26.51 ± 0.88 5.11 × 10−15 (1.35 ± 0.05) × 10−13 −1.36+0.03−0.03 0.73+0.16

−0.16 −6.79+0.15−0.16

MWC 297 I −455.84 ± 1.41 3.50 ± 0.02 −459.34 ± 1.41 4.81 × 10−14 (2.21 ± 0.01) × 10−11 1.99+0.05−0.04 4.08+0.21

−0.20 −3.61+0.19−0.20

VV Ser II R −39.07 ± 0.10 8.04 ± 0.07 −47.11 ± 0.12 1.31 × 10−15 (6.15 ± 0.02) × 10−14 - - -

MWC 300 III B −140.04 ± 0.40 1.95 ± 0.06 −141.99 ± 0.40 1.35 × 10−15 (1.91 ± 0.01) × 10−13 1.07+0.14−0.11 3.16+0.26

−0.21 −4.56+0.25−0.24

AS 310 I 0.83 ± 0.04 4.13 ± 0.03 −3.29 ± 0.05 6.60 × 10−16 (2.17 ± 0.03) × 10−15 −0.52+0.14−0.11 1.57+0.22

−0.20 −6.23+0.21−0.22

PDS 543 I 0.16 ± 0.01 2.66 ± 0.02 −2.50 ± 0.02 1.42 × 10−14 (3.55 ± 0.02) × 10−14 0.34+0.14−0.11 2.43+0.22

−0.18 −5.33+0.15−0.13

HD 179218 I −1.70 ± 0.05 12.43 ± 0.13 −14.14 ± 0.14 3.12 × 10−15 (4.41 ± 0.05) × 10−14 −1.01+0.02−0.02 1.08+0.13

−0.13 −6.31+0.12−0.12

HD 190073 IV B −24.79 ± 0.50 10.60 ± 0.19 −35.39 ± 0.53 1.99 × 10−15 (7.05 ± 0.11) × 10−14 0.22+0.10−0.08 2.31+0.18

−0.15 −4.97+0.18−0.14

V1685 Cyg II B −107.70 ± 0.67 3.63 ± 0.03 −111.33 ± 0.67 2.63 × 10−15 (2.93 ± 0.02) × 10−13 0.88+0.05−0.04 2.97+0.15

−0.14 −4.77+0.09−0.15

LkHA 134 I −68.47 ± 0.36 9.64 ± 0.08 −78.11 ± 0.37 6.45 × 10−16 (5.04 ± 0.02) × 10−14 0.05+0.04−0.03 2.14+0.10

−0.10 −5.28+0.11−0.10

HD 200775 II R −66.71 ± 0.23 5.21 ± 0.06 −71.92 ± 0.24 1.36 × 10−14 (9.76 ± 0.04) × 10−13 - - -

LkHA 324 II R −2.54 ± 0.03 7.74 ± 0.13 −10.28 ± 0.13 7.60 × 10−16 (7.81 ± 0.10) × 10−15 −1.05+0.03−0.03 1.04+0.14

−0.14 −6.48+0.13−0.15

HD 203024 I 8.88 ± 0.04 14.42 ± 0.20 −5.54 ± 0.20 8.72 × 10−16 (4.83 ± 0.18) × 10−15 - - -

V645 Cyg I −99.65 ± 1.32 2.15 ± 0.05 −101.80 ± 1.33 4.39 × 10−16 (4.47 ± 0.06) × 10−14 - - -

V361 Cep I −30.74 ± 0.24 5.11 ± 0.06 −35.85 ± 0.25 1.05 × 10−15 (3.75 ± 0.03) × 10−14 −0.03+0.04−0.03 2.06+0.10

−0.10 −5.54+0.10−0.10

V373 Cep III B −55.39 ± 0.39 7.40 ± 0.15 −62.80 ± 0.42 5.10 × 10−16 (3.21 ± 0.02) × 10−14 - - -

V1578 Cyg III B −19.29 ± 0.06 10.30 ± 0.09 −29.59 ± 0.11 7.77 × 10−16 (2.30 ± 0.01) × 10−14 −0.37+0.04−0.03 1.72+0.11

−0.11 −5.67+0.10−0.10

LkHA 257 I −5.40 ± 0.00 12.92 ± 0.25 −18.32 ± 0.25 8.56 × 10−17 (1.57 ± 0.02) × 10−15 −1.51+0.03−0.02 0.58+0.16

−0.16 −6.95+0.17−0.18

SV Cep III R 2.18 ± 0.16 14.89 ± 0.45 −12.71 ± 0.48 2.08 × 10−16 (2.65 ± 0.10) × 10−15 −2.01+0.03−0.03 0.08+0.19

−0.19 −7.46+0.19−0.17

V375 Lac IV B −18.88 ± 0.21 12.37 ± 0.02 −31.24 ± 0.21 9.02 × 10−17 (2.82 ± 0.02) × 10−15 - - -

HD 216629 II B −17.02 ± 0.09 3.68 ± 0.04 −20.70 ± 0.10 5.84 × 10−15 (1.21 ± 0.01) × 10−13 0.39+0.03−0.03 2.48+0.12

−0.11 −5.17+0.10−0.09

V374 Cep II B −32.95 ± 0.31 4.62 ± 0.05 −37.56 ± 0.31 3.09 × 10−15 (1.16 ± 0.01) × 10−13 0.44+0.04−0.04 2.53+0.13

−0.12 −4.95+0.11−0.10

V628 Cas IV B −124.89 ± 2.44 2.10 ± 0.01 −126.99 ± 2.44 6.52 × 10−15 (8.28 ± 0.16) × 10−13 - - -

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The final set of 78 mass accretion rates (21+57) basedon the INT and X-Shooter data is the largest, and arguablythe best such collection to date as they were determinedin a homogeneous and consistent manner. To arrive at thelargest sample possible however, we expand the sample usingdata provided in the comprehensive study by V18. Adding85 objects from V18 results in a large sample of 163 HerbigAe/Be stars with mass accretion rates4

5 ANALYSIS

We have obtained new spectroscopic data of 30 northernHerbig Ae/Be stars which are used to determine their stel-lar parameters, extinction and Hα emission line fluxes. Com-bined with Gaia DR2 parallaxes, this led to the determina-tion of the mass accretion rates for 21 of these objects. Thisdataset complements the large southern sample of F15, forwhich we re-determined stellar parameters using the Gaiaparallaxes and extinctions in the same manner as for thenorthern sample. This full sample contains 78 objects withhomogeneously determined values. To this we add 85 objectsfrom the V18 study for which literature values have beenadapted and new Hα line measurements have been addedusing data from archives. This led to a total of 163 objectsfor which we have stellar parameters, distances, Hα emis-sion line fluxes and mass accretion rates derived from theseusing the MA paradigm available. In the following we willinvestigate the dependence of the MA-derived accretion rateon stellar mass, and find that there is a break in propertiesaround 4M� .

5.1 Accretion luminosity as a function of stellarluminosity

Before addressing the mass accretion rate, let us first dis-cuss the accretion luminosity, as that is less dependenton the stellar parameters. In Figure 6 we show the accre-tion luminosity versus the stellar luminosity for the entiresample. The accretion luminosity increases monotonicallywith stellar luminosity, which confirms earlier reports (F15,Mendigutıa et al. 2011b). However, the sample under con-sideration is much larger than previously.

It would appear that the slope decreases, while the scat-ter in the relationship increases, with mass. To investigatewhether there is a significant difference in accretion lumi-nosities between high- and low mass objects, and if so, todetermine the mass where there is a turn-over, we split thedata into a low mass and a high mass sample, with a varying

4 When drafting this manuscript, a paper by Arun et al. (2019)

was published reporting on the accretion rates using Gaia dataof a somewhat smaller sample than here. Notable differences are

that we use homogeneously determined stellar parameters for alarge fraction of the sample and the fact that their sample is notselected for parallax quality and therefore includes faulty Gaia

parallax measurements affecting the derived distances. It wouldalso appear that their determination of the Hα line luminosity

does not account for underlying absorption, which will affect espe-cially the weakly emitting sources. As the authors do not provideall relevant datatables, it proved hard to investigate and assess

further differences.

turnover mass. We then fitted a straight line to the data fromthe lowest mass to this intermediate mass, and a straight linefrom the intermediate mass to the largest mass. The inter-mediate mass was varied from the second smallest to thesecond largest mass.

This resulted in values of the slopes and their statisticaluncertainty for a range of masses. When taking the differ-ence in slopes and expressing this in terms of the respectiveuncertainties in the fit, we arrive at a statistical assessmentwhether the low- and high mass samples have a differentslope. This approach takes into account the issue that theabsolute value of the difference-in-slopes may not be a reli-able indicator of the turn-over point. This is because eachslope can vary depending on both the number and spreadof data points used. For example, at both the high and lowmass ends, the slopes will have a large uncertainty simplybecause of small number statistics.

We quantify the difference in slopes by combining theuncertainties on both low and high mass gradients, σ, andcompare this to the difference in slopes, ∆(slope). This isshown in the top panel of Figure 6. The ∆(slope) reachesits maximum significance of 4σ for a luminosity of 194 L� ,which was determined by a triple-Gaussian fit to the curve.For the lower mass HAeBes, the linear best fit provides the

empirical calibration of log(LaccL�

)= (−0.87 ± 0.11) + (1.03 ±

0.08) × log(L∗L�

). This is in agreement with the best fit

for low-mass stars in the work of Mendigutıa et al. (2011b)(Lacc ∝ L1.2

∗ ). For the higher mass HAeBes, the best fit pro-

vides the expression of log(LaccL�

)= (0.19 ± 0.27) + (0.60 ±

0.08) × log(L∗L�

).

5.2 Mass accretion rate as a function of stellarmass

One of the main questions regarding the formation of mas-sive stars is at which mass the mass accretion mechanismchanges from magnetically controlled accretion to anothermechanism, which could be direct accretion from the diskonto the star. Above we saw that there is a difference inthe accretion luminosity to stellar luminosity relationshipsfor different masses. So, we now move to look at the massaccretion rates and investigate various subsamples individ-ually.

Let us first consider the sample with homogeneouslyderived mass accretion rates, before investigating the fullsample. The relationship between mass accretion rate andstellar mass of the combined sample from this work andFairlamb et al. (2015, 2017) that are present in The et al.(1994, table 1), is shown in the left hand panel of Figure 7.The sample of The et al. (1994), contains the best estab-lished HAeBes, and is thus least contaminated by possiblemisclassified objects. It can be seen that the mass accretionrate increases with stellar mass, and that there is a differentbehaviour for objects with masses below and above the massrange with log(M∗) = 0.4–0.6. This break is consistent withthe major finding in F15 that the relationship between massaccretion rate and stellar mass shows a break around theboundary between Herbig Ae and Herbig Be stars. In par-ticular, they found that the relationship between mass ac-

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Figure 5. The placement of all 163 HAeBes in the HR diagram. The PMS tracks with initial mass from 1 to 40 M� (Bressan et al. 2012;

Tang et al. 2014) and isochrones of 0.01, 0.1, 1 and 10 Myr (Marigo et al. 2017) are plotted as solid and dashed lines respectively. The

colour map denotes the accretion rate.

cretion rate and mass has a different slope for the lower andhigher mass objects respectively. With our improved samplein hand, we can now revisit this finding and we determinethe mass at which the break occurs with higher precision inthe same way as we found the turnover luminosity earlier.

We found that the maximum slope difference is at the4.4σ level for the The et al. sample at log(M∗) = 0.56+0.14

−0.14or M∗ = 3.61+1.38

−0.98 M�. The uncertainty in the mass is de-cided where the difference in slope is 1σ smaller than atmaximum. If we focus on the total combined sample of 78objects from this work and F15, the break is established atlog(M∗) = 0.58+0.14

−0.14 or M∗ = 3.81+1.46−1.05 M� with the maxi-

mum gradient difference about 6.4σ. as shown in the mid-dle panel of Figure 7. It can be seen that this plot showsthe same relationship as the one in the left-hand panel.When considering the full, combined sample of 163 objectsfrom this work, F15 and V18 whose mass accretion rates areshown in the right-hand panel of Figure 7, the break is nowfound at the log(M∗) = 0.60+0.13

−0.12 or M∗ = 3.98+1.37−0.94 M� with

the maximum difference of gradient about 6.6σ.

We note that both the significance of the difference inslopes as well as the mass at which the break occurs increaseswith the number of objects. This could be due to the num-

ber of objects; especially as the The et al. (1994) sample issparsely populated at the high mass end, which could in-crease the uncertainty on the resulting slope and thus lowerthe significance of the difference in slopes between high andlow mass objects. Alternatively, it could be affected by alarger contamination of non-Herbig Be stars in the full sam-ple. It is notoriously hard to differentiate between a regularBe star and a Herbig Be star. Given the low number statis-tics of the The et al. (1994) sample and the similarity of thebreak in mass of the other two samples, we will proceed witha break in slope at 4 M� .

5.2.1 Literature comparisons with T Tauri stars

It is interesting to see how the accretion luminosities com-pare to those of T Tauri stars at the low mass range. Withthe large caveat that no Gaia DR2 study of T Tauri stars andtheir stellar parameters and accretion rates exists at the mo-ment, we show in Figure 8 the Lacc against L∗ for the wholesample of 163 HAeBes in this work compared to classicalT Tauri stars of which all luminosity values are taken fromHartmann et al. (1998), White & Basri (2003), Calvet et al.(2004) and Natta et al. (2006). On one hand, the gradient

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Figure 6. The logarithmic accretion luminosities versus stellar

luminosities for the full, 163 stars, sample. Also shown are lin-ear fits to the full sample and to the low- and high-mass stars

respectively. As can be seen in the top panel, the difference in

slopes between the low- and high-mass objects is most significantat at L∗ > 194 L� (see text for details). The gradients of best

fits for the whole sample, low-mass and high-mass HAeBes are0.85 ± 0.03, 1.03 ± 0.08 and 0.60 ± 0.08 respectively.

of best fit for the classical T Tauri stars is 1.17 ± 0.09 whichis close, and well within the errorbars, to 1.03± 0.08 for low-mass HAeBes. On the other hand, high-mass HAeBes showsa flatter relationship of Lacc ∝ L0.60±0.08

∗ . It would seem thatthe Herbig Ae and Be stars with masses up until 4 M� be-have similarly to the T Tauri stars. Again, stellar parametersof these classical T Tauri stars were not derived in the samemanner as HAeBes in this work. This may have an effect onour conclusion.

5.3 Mass accretion rate as a function of stellar age

In Figure 5 we illustrate the mass accretion rates across theHR-diagram. As expected, it can be seen that the accretionrates are largest for the brightest and most massive objects.However, the sample may allow an investigation into theevolution of the mass accretion rate as a function of stellarage as provided by the evolutionary models. In general it canbe stated that, in terms of evolutionary age, the youngerobjects have higher accretion rates than older objects. Asillustration, we show the mass accretion rate as a function ofage in the top panel of Figure 9. It is clear that the accretionrate decreases with age (as also shown in F15); the Pearsoncorrelation coefficient is -0.87.

However, when considering any properties as a functionof age, there is always the issue that higher mass stars evolvefaster than lower mass stars. Hence, the observed fact that

higher mass objects have higher accretion rates could be themain underlying reason for a trend of decreasing accretionrate with time. Indeed, in the top panel of Figure 9 therange in accretion rates covers the entire accretion range ofthe accretion vs. mass relation, so it is hard to disentanglefrom this graph whether there is also an accretion rate - agerelation.

This can in principle be circumvented when selecting asample of objects in a small mass range, so that the spreadin mass accretion rates is minimized. This needs to be offsetagainst the number of objects under consideration. In thelower panels of Figure 9 we show how the accretion ratechange with the age of stars in 3 different mass bins (2.0-2.5 M�, 2.5-3.0 M� and 3.0-3.5 M�. A best fit taken intoaccount the uncertainties in both the mass accretion rateand age to the 30 objects where 2.0 M� < M∗ < 2.5 M�shows a Macc ∝ Age−1.95±0.49 with a Pearson’s correlationcoefficient -0.55. The 9 stars with masses 2.5 M� < M∗ <3.0 M� have a gradient of a best fit is −1.40±1.47 (correlationcoefficient 0.40). The error of the best fit gradient becomesslightly larger than its own value, which is due to the smallernumber of objects involved. The 8 objects with 3.0 M� <

M∗ < 3.5 M� in the bottom panel of Figure 9 have a gradientof a best fit is −0.37 ± 1.25 with a linear correlation -0.36.It can be seen that the error of the best fit gets larger than3 times of its own absolute value. This is more likely to bedue to the lack of HAeBes when the stellar mass increases.

The 2.0-2.5 M� sample is best suited to study any trendin accretion rate with age in the sense that the accretionrates change by 0.4 dex across this mass range (cf. the slopeof 4.05 found for the low mass objects in Sec. 5.2). Thespread in accretion rates in the graph is twice that, and ifthe additional decrease in mass accretion rate is due to evo-lution, we find Macc ∝ Age−1.95±0.49. This value is the onlysuch determination for Herbig Ae/Be stars in a narrow massrange, other determinations were based on full samples ofHAeBe stars which contain many different masses and suf-fer from a mass-age degeneracy (e.g. F15, Mendigutıa et al.(2012)). Despite the relatively large errorbars, we note thatour determination is remarkably close to the observed val-ues for T Tauri stars by Hartmann et al. (1998), who findan η between 1.5-2.8, while theoretically these authors pre-dict η to be larger than 1.5 for a single α viscous disk. Wealso refer the reader to the discussion in Mendigutıa et al.(2012), who, remarkably, find a similar value of the exponentto ours: 1.8+1.4

−0.7 as determined for their full sample.

6 DISCUSSION

In the above we have worked out the mass accretion ratesfor a large sample of 163 Herbig Ae/Be stars. To this endnew and spectroscopic archival data were employed. A largefraction of the sample now has homogeneously determinedastrophysical parameters, while Gaia parallaxes were usedto arrive at updated luminosities for the sample objects. Wecompared the mass accretion rates derived using the MAparadigm for Herbig Ae/Be stars with various properties.We find that:

• The mass accretion rate increases with stellar mass, butthe sample can be split into two subsets depending on theirmasses.

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Figure 7. The difference of the gradient of the best fits between the low-mass and the high-mass HAeBes in terms of the uncertainty

of the gradient difference (top panel) and the mass accretion rates versus stellar masses (bottom panel). Left: 43 stars from this worksample and the sample of Fairlamb et al. (2015) presents in table 1 of The et al. (1994). Objects are separated into the low-mass HAeBes,

M∗ < 3.61 M� , and the high-mass HAeBes, M∗ > 3.61 M� . The slopes of best fits for the whole sample, low-mass and high-mass HAeBes

are 2.94 ± 0.24, 4.72 ± 0.49 and 1.20 ± 0.65 respectively. Middle: 78 objects from this work sample and the sample of Fairlamb et al.(2015). The break is defined at M∗ = 3.81 M� . The gradients of best fits for the whole sample, low-mass and high-mass HAeBes are

2.60±0.19, 4.78±0.34 and 1.14±0.46 respectively. Right: 163 objects are separated into the low-mass HAeBes and the high-mass HAeBes

at M∗ = 3.98 M� . The gradients of best fits for the whole sample, low-mass and high-mass HAeBes are 2.67 ± 0.13, 4.05 ± 0.24 and1.26 ± 0.34 respectively.

• The low mass Herbig Ae stars’ accretion rates have asteeper dependence on mass than the higher mass Herbig Bestars.• The above findings corroborate previous reports in the

literature. The larger sample and improved data allows usto determine the mass where the largest difference in slopesbetween high and low mass objects occurs. We find it is 4M� .• Bearing in mind the caveat that T Tauri stars do not yet

have Gaia based accretion rates, it appears that the HerbigAe stars’ accretion properties display a similar dependenceon luminosity as the T Tauri stars.• In general, younger objects have larger mass accretion

rates, but it proves not trivial to disentangle a mass depen-dence from an age dependence. We present the first attemptto do so. A small subset in a narrow mass range leads us tosuggest that the accretion rate decreases with time.

In the following we aim to put these results into context,but we start by discussing the various assumptions that hadto be made to arrive at these results.

6.1 On the viability of the MA model todetermine accretion rates of Herbig Ae/Bestars

In the above we have determined accretion luminosities andaccretion rates to young stars. However, the question re-mains whether the magnetic accretion shock modelling thatunderpins these computations should be applicable. Afterall, A and B-type stars typically do not have magnetic fielddetections, and indeed, are not expected to harbour mag-netic fields as their radiative envelopes would not create

a dynamo that in turn can create a magnetic field. Thiswas verified in a study of Intermediate Mass T Tauri stars(IMTTS) by Villebrun et al. (2019) who found that the frac-tion of pre-Main Sequence objects with a magnetic field de-tection drops markedly as they become hotter (for similarmasses). These authors suspect that any B-field detectionsin Herbig Ae/Be stars could be fossil fields from the evolu-tionary stage immediately preceding them. The fields wouldnot only be weaker, but also more complex, hampering theirdirect detection.

Muzerolle et al. (2004) showed that the MA models pro-vided qualitative agreement with the observed emission lineprofiles of the Herbig Ae star UX Ori. In the process, theyalso found that the B-field geometry should be more complexthan the usual dipole field in T Tauri stars and the expectedfield strength would be much below the usual T Tauri de-tections, in line with the Villebrun et al. (2019) findings.

Since, based on statistical studies and targeted indi-vidual investigations evidence has emerged that Herbig Aestars are similar to the T Tauri stars. Garcia Lopez et al.(2006) showed that the accretion rate properties of the Her-big Ae stars constitute a natural extension to the T Tauristars, while F15 demonstrated that the MA model can repro-duce the observed UV excesses towards most of their HerbigAe/Be stars with realistic parameters for the shocked re-gions. A small number of objects, all Herbig Be stars, couldnot be explained with the MA model. They exhibit sucha large UV-excess that they would require shock coveringfactors larger than 100%, which is clearly unphysical.

Vink et al. (2002) and Vink et al. (2005) were the firstto point out the remarkable similarity in the observed linearspectropolarimetric properties of the Hα line in Herbig Ae

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Figure 8. Accretion luminosity versus stellar luminosity for163 HAeBes in this work and classical T Tauri stars from

Hartmann et al. (1998), White & Basri (2003), Calvet et al.

(2004) and Natta et al. (2006). Red, green and blue dashedlines are the best fit for T Tauri stars (Lacc ∝ L1.17±0.09

∗ ), low-

mass HAeBes (Lacc ∝ L1.03±0.08∗ ) and high-mass HAeBes (Lacc ∝

L0.60±0.08∗ ) respectively.

stars and T Tauri stars. The polarimetric line effects in thesetypes of objects can be explained with geometries consistentwith light scattering off (magnetically) truncated disks. Incontrast, the very different effects observed towards the Her-big Be stars were more consistent with disks reaching ontothe central star - hinting at a different accretion mechanismin those. The large sample by Ababakr et al. (2017) allowedthem to identify the transition region to be around spectraltype B7/8.

Cauley & Johns-Krull (2014) studied the He i 1.083 µmline profiles of a large sample of Herbig stars and found thatboth T Tauri and Herbig Ae stars could be explained withMA, while the Herbig Be stars could not. Reiter et al. (2018)did not detect a difference in line morphology between thefew (5) magnetic Herbig Ae/Be stars and the rest of thesample. They argued that Herbig Ae stars may thereforenot accrete similarly to T Tauri stars. However, based onPoisson statistics alone, even if all magnetic objects showedeither a P Cygni or Inverse P Cygni profile, a sample of5 would not be sufficient to conclusively demonstrate thatthe magnetic objects are, or are not, different from the non-magnetic objects. Clearly, more work needs to be done inthis area. Costigan et al. (2014) investigated the Hα linevariability properties of Herbig Ae/Be stars and T Tauristars and found that both the timescales and amplitude ofthe variability were similar for the Herbig Ae and T Tauri,which also led these authors to suggest that the mode of ac-cretion of these objects are similar. A notion also implied byour result in Figure 8 that the accretion luminosities of bothHerbig Ae and T Tauri stars appear to have the same depen-dence on the stellar luminosity. Finally, Mendigutıa et al.

Figure 9. Ages versus mass accretion rates. From top to bot-tom all sample, the mass range 2.0-2.5 M� , 2.5-3.0 M� and 3.0-

3.5 M� . The best fit is shown in the dashed line where Macc ∝

Age−1.11±0.05, Macc ∝ Age−1.95±0.49, Macc ∝ Age1.40±1.47 andMacc ∝ Age−0.37±1.25 respectively. The colour map indicates stel-

lar mass of each mass bin.

(2011a) found that the Hα line width variability of HerbigBe stars is considerably smaller than for Herbig Ae stars,which is in turn smaller than for TTs (see Figure 37 inFang et al. 2013). This may suggest smaller line emittingregions/magnetospheres as the stellar mass increases, andthus a eventual transition from MA to some other mecha-nism responsible for accretion.

To summarize this section, various studies of differentobservational properties have confirmed the many similar-ities between T Tauri and Herbig Ae stars, which in turnhint at a similar accretion mechanism, the magnetically con-trolled accretion. In turn, this would validate our use of theMA shock modelling to derive mass accretion rates for atleast the lower mass end of the Herbig Ae/Be star range.Before we discuss the accretion mechanisms for low- andhigh mass stars, we address the use of line luminosities toarrive at accretion luminosities and rates below.

6.2 On the use of line emission as accretion ratediagnostic

The only “direct” manner to determine the mass accretionrate is to measure the accretion luminosity, which is essen-tially the amount of gravitational potential energy that isconverted into radiation at ultra-violet wavelengths. Thiscan then be turned into a mass accretion rate once the stel-lar mass and radius are known. The determination of the

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contribution of the accretion shock to the total UV emissionfor HAeBe objects is not straightforward due to the fact thatthese stars intrinsically emit many UV photons by virtue oftheir higher temperatures.

Calvet et al. (2004) showed that the Brγ emissionstrengths observed towards a sample of IMTTS correlatedwith the accretion luminosity as determined by the UV ex-cess for a large mass range extending to 3.7 M� (the massof their most massive target, GW Ori, with spectral typeG0 - cool enough to unambiguously determine the UV ex-cess emission). This was already known for lower mass ob-jects, but, significantly, these authors extended it to highermasses. In addition, these authors also showed that the massaccretion rate correlated with the stellar mass over this massrange. Therefore they also demonstrated that line emission,in this case the hydrogen recombination Brγ, can be used tomeasure accretion rates to masses of at least up to ∼4 M� .Mendigutıa et al. (2011b) measured the UV-excess of Her-big Ae/Be stars using UV-blue spectroscopy and photome-try respectively and noted the correlation with emission linestrengths (see also Donehew & Brittain 2011). F15 and F17took this further and demonstrated the strong correlationbetween emission line strength and accretion luminosity fora much larger sample and a mass range going up to 10–15M� . It extended to an accretion luminosity of 104 L� andwas shown to hold for a large number of different emissionlines.

One should keep in mind the caveat, also pointed outby F17, that high spatial resolution optical and near-infraredstudies of the hydrogen line emission do not necessarily iden-tify the line emitting regions of Herbig Ae/Be stars withthe magnetospheric accretion channels. Already in 2008,Kraus et al. (2008) reported that their milli-arcsec resolu-tion AMBER interferometric data indicated different Brγline forming regions which were consistent with the MA sce-nario for some objects but with disk-winds for others. Fur-ther studies by e.g. Mendigutıa et al. (2015b) find the lineemission region consistent with a rotating disk. Similarly,Tambovtseva et al. (2016) and Kreplin et al. (2018) find thedisk-wind a more likely explanation for the emitting regionthan the compact accretion channels. Even higher resolu-tion Hα CHARA data discussed by Mendigutıa et al. (2017)present a similar diversity.

There thus remains the question whether we can useemission lines to probe accretion if they are apparently notrelated to the accretion process itself, or indeed, why the lineluminosities correlate with the accretion luminosity at all. Itis well known that accretion onto young stars drives jets andoutflows, where the mass ejection rates are of order 10% ofthe accretion rates (see e.g. Purser et al. 2016). If this is alsothe case for Herbig Ae/Be stars, then one could expect theemission lines to be correlated with the accretion rates. Onthe other hand, Mendigutıa et al. (2015a) pointed out thatwhile the physical origin of the lines may not be relatedto the accretion process per se, it is the underlying corre-lation between accretion luminosity and stellar luminositythat gives rise to a correlation between the line strengthsand accretion. Hence, although the lines may not necessarilybe directly accretion-related, the empirical correlations be-tween emission line luminosities and accretion luminositiesare strong enough to validate their use as accretion tracers.

When we revisit the various studies mentioned above, it

is notable that a distinction between Herbig Ae and HerbigBe stars is found, spectroscopically (Cauley & Johns-Krull2014), spectropolarimetrically (Vink et al. 2005), due tospectral variability (Costigan et al. 2014), and even whenconsidering the accretion rates from UV-excesses (F15).

Based on the break in accretion rates, we can move thisboundary to a critical mass of 4M� , remarkably close, butnot perfectly so, to the boundary of around B7/8 put for-ward by Ababakr et al. (2017). It is thus implied that thereis a transition from magnetically controlled accretion in low-mass HAeBes to another accretion mechanism in high-massHAeBes at around 4 M�. The remaining question is whatthis mechanism should be.

6.3 If MA does not operate in massive objects,what then?

The spectropolarimetric finding of a disk reaching ontothe star is reminiscent of the Boundary Layer (BL) ac-cretion mechanism that was found to be a natural conse-quence of a viscous circumstellar disk around a stellar ob-ject (Lynden-Bell & Pringle 1974). The BL is a thin an-nulus close to the star in which the material reduces its(Keplerian) velocity to the slow rotation of the star whenit reaches the stellar surface. It is here that kinetic energyand angular momentum will be dissipated. The BL mech-anism was originally used to explain the observed UV ex-cesses of low mass pre-Main Sequence stars (Bertout et al.1988) until observations led to strong support for the mag-netic accretion scenario instead (Bouvier et al. 2007). One ofthe difficulties the BL mechanism had was the smaller red-shifted absorption linewidths predicted from the Keplerianwidths expected from the BL than from freefall in the caseof MA (Bertout et al. 1988). It had been suggested in thepast to operate in Herbig Ae/Be objects (eg Blondel & Djie2006 who studied Herbig Ae stars; Mendigutıa et al. 2011b;Cauley & Johns-Krull 2014) but has never been adapted andtested for masses of Herbig Be stars and greater.

It is very much beyond the scope of this paper to ad-dress the BL theoretically, but let us suffice with a basicconsideration to see whether we would be able to expect adifferent slope in the derived accretion rate or luminosity foran object undergoing MA or BL accretion. In both situationsinfalling material converts energy into radiation. In MA theenergy released by a mass dM falling onto a star with massand radius M∗ and R∗ respectively will be the gravitationalpotential energy of the infalling material, GM∗dM

R∗, times a

factor close to 1 accounting for the fact that material is notfalling from infinity.

How would this amount of released energy compare tothat in the BL scenario for infalling material of the samemass dM? For the BL case, the accretion energy will be atmost the kinetic energy of the rotating material prior tobeing decelerated in the very thin layer close to the stellarsurface. As the material rotates Keplerian, we know that the

centripetal force equals the force of gravity, dMv2

R∗=

GM∗dM

R2∗

.

We thus find that the kinetic energy 12 dMv2 =

GM∗dM2R∗

,which is half the gravitational potential energy for the samemass.

In other words, the energy released in the BL scenariowill be less than that released by MA for the same mass.

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Therefore if the mass accretion rate is the same, we obtaina lower accretion luminosity for objects accreting materialthrough a Boundary Layer than through MagnetosphericAccretion. This also means that the accretion rate has tobe larger in BL to arrive at the same accretion luminosity.In turn, this has as implication that if we derive the massaccretion rates using the MA paradigm, while the accretionis due to BL, then the resulting accretion luminosities andrates would have been underestimated.

Earlier, we found that the (MA derived) accretion lumi-nosities have the same dependence of the accretion luminos-ity on the stellar luminosity for T Tauri stars and Herbig Aestars, while we find a smaller gradient for the more massivestars. If we would assume that this dependence would holdfor more massive stars too, then it could be concluded thatthe accretion rates have been underestimated for massiveHerbig Be stars. If the BL scenario was the acting mecha-nism for the Herbig Be stars then the accretion luminositieswould be larger - possibly resulting in the same relationshipbetween accretion and stellar luminosity as the lower massstars, and no break would be visible.

Could that be the case here? The accretion onto thestars likely depends on the rates the accretion disks are fedand mass needs to be transported through the disk, so itmay be reasonable to assume that this process is less de-pendent on the stellar parameters and a simple correlationbetween accretion onto the star and stellar luminosity (ormass) would be expected. It is intriguing that the BL sce-nario for more massive stars might explain why we obtainlower accretion rates when we assume MA for the more mas-sive objects resulting in a break at around 4 M�. An in-depthinvestigation into the BL is certainly warranted.

7 FINAL REMARKS

In this paper we presented an analysis of a new set of opticalspectroscopy of 30 northern Herbig Ae/Be stars. This wascombined with our data and analysis of southern objects inF15 resulting in a set of temperatures, gravities, extinctionsand luminosities that were derived in a consistent manner.As such this constitutes the largest homogeneously analysedsample of 78 Herbig Ae/Be stars to date. To these we added85 objects from the Gaia DR2 study of V18. The total sam-ple of 163 objects allowed us to derive the accretion luminosi-ties and mass accretion rates using the empirical power-lawrelationship between accretion luminosity and line luminos-ity as derived under the MA paradigm.

We identified a subset in the total sample as being thestrongest Herbig Ae/Be star candidates known. The set con-tains 60 per cent of the objects in Table 1 from the The et al.(1994) catalogue. All trends found in the large sample arealso present in this subsample. This implies that the largesample likely has a low contamination and is therefore agood representation of the Herbig Ae/Be class.

• We find that the mass accretion rate increases with stel-lar mass, and that the lower mass Herbig Ae stars’ accretionrates have a steeper dependence on mass than the highermass Herbig Be stars. This confirms previous findings, butthe large sample allows us to determine the mass where thisbreak occurs. This is found to be 4 M�.

• A comparison of accretion luminosities of the HerbigAe/Be stars with those of T Tauri stars from the literatureindicates that the Herbig Ae stars’ accretion rates displaya similar dependence on luminosity as the T Tauri stars.This provides further evidence that Herbig Ae stars mayaccrete in a similar fashion as the T Tauri stars. We docaution however that T Tauri stars do not yet have Gaia-based accretion rates.• We also find that in general, younger objects have larger

mass accretion rates. However, it is not trivial to disentanglea mass and age dependence from each other: More massivestars have larger accretion rates, but have much smaller agesas well. A small subset selected in a narrow mass range leadsus to suggest that the accretion rate does indeed decreasewith time. The best value could be determined for the massrange 2.0-2.5 M� . We find Macc ∝ Age−1.95±0.49.

Finally, we discussed the similarities and differences be-tween the accretion properties of lower mass and higher massHerbig pre-Main Sequence stars. In particular we discuss thevarious lines of evidence that suggest they accrete in dif-ferent fashions. In addition, from linear spectropolarimetricstudies, the Herbig Be stars are found to have disks reachingonto the stellar surface while the Herbig Ae stars (with thebreak around 4 M�) have disks with inner holes, similar tothe T Tauri stars.

We therefore put forward the Boundary Layer mech-anism as a viable manner for the accretion onto the stel-lar surface of massive pre-Main Sequence stars. More workneeds to be done, but an initial, crude, estimate of the ac-cretion luminosity dependency on mass – assuming a globalcorrelation between mass accretion rate and stellar mass forall masses – can explain the observed break in accretionproperties.

ACKNOWLEDGEMENTS

The authors would like to thank to the anonymous reviewerwho provided constructive comments which helped improvethe manuscript. CW thanks Thammasat University forfinancial support in the form of a PhD scholarship atthe University of Leeds. IM acknowledges the funds froma “Talento” Fellowship (2016-T1/TIC-1890, Governmentof Comunidad Autonoma de Madrid, Spain). M. Vioquewas funded through the STARRY project which receivedfunding from the European Union’s Horizon 2020 re-search and innovation programme under MSCA ITN-EIDgrant agreement No 676036. This work has made use ofdata from the European Space Agency (ESA) missionGaia (https://www.cosmos.esa.int/gaia), processed bythe Gaia Data Processing and Analysis Consortium (DPAC,https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national insti-tutions, in particular the institutions participating in theGaia Multilateral Agreement. This research has made useof IRAF which is distributed by the National Optical As-tronomy Observatory, which is operated by the Associationof Universities for Research in Astronomy (AURA) under acooperative agreement with the National Science Founda-tion. This publication has made use of SIMBAD data base,operated at CDS, Strasbourg, France. It has also made useof NASA’s Astrophysics Data System and the services of

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the ESO Science Archive Facility. Based on observationscollected at the European Southern Observatory underESO programmes 60.A-9022(C), 073.D-0609(A), 075.D-0177(A), 076.B-0055(A), 082.A-9011(A), 082.C-0831(A),082.D-0061(A), 083.A-9013(A), 084.A-9016(A) and 085.A-9027(B). This research was made possible through theuse of the AAVSO Photometric All-Sky Survey (APASS),funded by the Robert Martin Ayers Sciences Fund and NSFAST-1412587.

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8 SUPPORTING INFORMATION

Supplementary appendices are available for down-load alongside this article on the MNRAS website(https://academic.oup.com/mnras).

APPENDIX A: STANDARD STARS

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Table A1. Log of observations of standard stars. Column 1 gives the object name. Columns 2 and 3 are right ascension (RA) in the units of time (.h .m .s) and declination (DEC) in the

units of angle (.◦ .′ .′′) respectively, column 4 lists the observation dates. Columns 5–7 present the exposure times for each grating. The signal-to-noise ratios for each grating are givenin columns 8–10. Spectral type is listed along with references in columns 11–12. The entire table is available online as supplementary material.

Name RA DEC Obs Date Exposure Time (s) SNR Spectral Type

(J2000) (J2000) (June 2013) R1200B R1200Y R1200R R1200B R1200Y R1200R Ref.

Feige 98 14:38:15.8 +27:29:33.0 23 - 300 - - 94 - sdB9III:He1 1

HD 130109 14:46:14.9 +01:53:34.4 21; 23 60; 20 20 - 179 420 - A0 IIInn 2

BD+26 2606 14:49:02.4 +25:42:09.2 23 - 150 - - 124 - A5 3

... ... ... ... ... ... ... ... ... ... ... ...

References: (1) Drilling et al. (2013); (2) Abt & Morrell (1995); (3) Fulbright (2000); (4) Morgan & Keenan (1973); (5) Cowley (1972); (6) Cowley et al. (1969); (7) Lesh (1968); (8)De Vaucouleurs (1957); (9) Hill & Lynas-Gray (1977); (10) Gray et al. (2003); (11) Hube (1970).

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Figure B1. The Hα line profiles for the 30 objects listed in Ta-ble 1. The entire figure is available online as supplementary ma-

terial.

APPENDIX B: THE Hα PROFILES

APPENDIX C: 91 HERBIG STARS IN THEFAIRLAMB ET AL. (2015) SAMPLE

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Table C1. Stellar parameters of 91 Herbig Ae/Be stars in the Fairlamb et al. (2015) sample. Column 1 gives the object name. Columns 2 and 3 are right ascension (RA) in the

units of time (.h .m .s) and declination (DEC) in the units of angle (.◦ .′ .′′) respectively. Columns 4–11 are effective temperature, surface gravity, visual extinction, distance, radius,

luminosity, mass and age respectively. Temperature and surface gravity are taken from Fairlamb et al. (2015). Distance is obtained from Vioque et al. (2018). The rest of parametersare redetermined in this work. The entire table is available online as supplementary material.

Name RA DEC Teff log(g) AV D R∗ log(L∗ ) M∗ Age

(J2000) (J2000) (K) [cm s−2] (mag) (pc) (R�) [L� ] (M�) (Myr)

UX Ori 05:04:29.9 -03:47:14.2 8500+250−250 3.90+0.25

−0.25 0.99+0.04−0.03 324.9+9.3

−8.4 1.80+0.09−0.08 1.18+0.09

−0.09 1.82+0.07−0.08 7.08+0.51

−0.47

PDS 174 05:06:55.5 -03:21:13.3 17000+2000−2000 4.10+0.40

−0.40 3.36+0.29−0.39 398+10

−9 1.12+0.23−0.23 1.98+0.35

−0.42 3.18+0.57−0.87 2.75+3.01

−1.13

V1012 Ori 05:11:36.5 -02:22:48.4 8500+250−250 4.38+0.15

−0.15 1.15+0.05−0.06 -d - - - -

... ... ... ... ... ... ... ... ... ... ...

Notes. (a) Stars which are also in this work’s sample. (b) Stars of which photometry were used for the photometry fitting different from values listed in Fairlamb et al. (2015, table A1)

(see text for details). (c ) Stars which have small emissions. (d) Stars which have low quality parallaxes in the Gaia DR2 Catalogue (see the text for discussion). (e) Stars which do nothave parallaxes in the Gaia DR2 Catalogue.

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Table C2. The equivalent width measurements and accretion rates of 91 Herbig Ae/Be stars in the Fairlamb et al. (2015) sample. Columns 2–9 present observed equivalent width,

intrinsic equivalent width, corrected equivalent width, continuum flux density at central wavelength of the Hα profile, line flux, line luminosity, accretion luminosity and mass accretion

rate respectively. Equivalent widths are taken from Fairlamb et al. (2017). The rest of parameters are redetermined in this work. The entire table is available online as supplementarymaterial.

Name EWobs EWint EWcor Fλ Fline log(Lline) log(Lacc) log(Macc)

(A) (A) (A) (W m−2 A−1) (W m−2) [L� ] [L� ] [M� yr−1]

UX Ori 2.39 ± 0.34 14.65 ± 1.47 −12.26 ± 1.51 4.03 × 10−16 (4.94 ± 0.61) × 10−15 −1.79+0.07−0.08 0.30+0.22

−0.23 −7.20+0.23−0.23

PDS 174 −54.19 ± 1.34 6.46 ± 0.65 −60.65 ± 1.49 3.59 × 10−16 (2.18 ± 0.05) × 10−14 −0.97+0.03−0.03 1.12+0.14

−0.14 −6.82+0.15−0.10

V1012 Ori 4.74 ± 0.55 16.36 ± 1.64 −11.62 ± 1.73 1.06 × 10−16 (1.23 ± 0.18) × 10−15 - - -

... ... ... ... ... ... ... ... ...

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APPENDIX D: 144 HERBIG STARS IN THEVIOQUE ET AL. (2018) SAMPLE

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Table D1. The equivalent width measurements and accretion rates of 144 Herbig Ae/Be stars in the Vioque et al. (2018) sample. Column 1 gives the object name. Columns 2 and 3 are

right ascension (RA) in the units of time (.h .m .s) and declination (DEC) in the units of angle (.◦ .′ .′′) respectively. Observed equivalent width is listed along with references in columns

4–5. The rest of parameters are derived in this work. Columns 6–12 present intrinsic equivalent width, corrected equivalent width, continuum flux density at central wavelength of theHα profile, line flux, line luminosity, accretion luminosity and mass accretion rate respectively. The entire table is available online as supplementary material.

Name RA DEC EWobs EWint EWcor Fλ Fline log(Lline) log(Lacc) log(Macc)

(J2000) (J2000) (A) Ref. (A) (A) (W m−2 A−1) (W m−2) [L� ] [L� ] [M� yr−1]

HBC 1 00:07:02.6 +65:38:38.3 −31.00 ± 3.10 1 14.43 ± 0.05 −45.43 ± 3.10 1.15 × 10−18 (5.24 ± 0.36) × 10−17 -a - -

HBC 324 00:07:30.6 +65:39:52.6 −16.90 ± 0.85 2 13.99 ± 0.11 −30.89 ± 0.85 2.42 × 10−17 (7.48 ± 0.21) × 10−16 -a - -

MQ Cas 00:09:37.5 +58:13:10.7 - - 15.82 ± 0.12 - 4.25 × 10−17 - -a - -

... ... ... ... ... ... ... ... ... ... ... ...

Notes. (a) Stars which have low quality parallaxes in the Gaia DR2 Catalogue (see the text for discussion). References: (1) Herbig & Bell (1988); (2) Hernandez et al. (2004); (3)

Mendigutıa et al. (2011a); (4) Pogodin et al. (2012); (5) ESO Programme 082.A-9011(A); (6) ESO Programme 076.B-0055(A); (7) Sartori et al. (2010); (8) Baines et al. (2006); (9)Miroshnichenko et al. (1999); (10) Boehm & Catala (1995); (11) Wheelwright et al. (2010); (12) Vieira et al. (2011); (13) Hernandez et al. (2005); (14) Oudmaijer & Drew (1999); (15)

ESO Programme 085.A-9027(B); (16) ESO Programme 082.D-0061(A); (17) ESO Programme 084.A-9016(A); (18) ESO Programme 083.A-9013(A); (19) Carmona et al. (2010); (20)

Spezzi et al. (2008); (21) Dunkin et al. (1997); (22) ESO Programme 075.D-0177(A); (23) ESO Programme 60.A-9022(C); (24) Borges Fernandes et al. (2007); (25) ESO Programme073.D-0609(A); (26) Ababakr et al. (2017); (27) Manoj et al. (2006); (28) Frasca et al. (2016); (29) Polster et al. (2012); (30) Kucerova et al. (2013); (31) Acke et al. (2005); (32)

Nakano et al. (2012); (33) Miroshnichenko et al. (2002); (34) Miroshnichenko et al. (2000); (35) Zuckerman et al. (2008).

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